where some lower-order logarithmic factors are ignored. Although the dependency of \(d\)  becomes polynomial (i.e., \(d^{3/2}\) ) in the new bound, the bound becomes trivial when \(d\ge \Omega (m^{1/3})\) , since the bound will not decrease with the growth of sample size \(m\)  in this case, indicating that it is not possible to reduce generalization error by increasing the size of training data. This is obviously not consistent with our observations during the training process of deep neural networks [1]}.
